In X-ray tomography, a three-dimensional image of the interior of an object is computed from multiple X-ray images, acquired over a range of angles. Two types of methods are commonly used to compute such an image: analytical methods and iterative methods. Analytical methods are computationally efficient, but in many applications, they produce reconstructions that are not accurate enough for further analysis. More accurate reconstructions can be obtained by using (regularized) iterative methods, but these can have computational costs that are too high to be used in practice. In this thesis, new reconstruction methods are developed that combine the analytical and algebraic approaches, resulting in methods that are as computationally efficient as analytical methods, but with a reconstruction accuracy of iterative methods. Analytical methods allow for changing their filter without increasing the needed computation time. We use this freedom in filter choice to develop new filter-based reconstruction methods, which are based on the analytical FBP method with specific filters. The filters can be defined and computed in different ways, and can depend on the acquisition geometry, the scanned object, and/or a separate pre-computing step. Several filter-based methods are introduced in this thesis and reconstruction results are compared with other popular methods.